If origin is the centroid of `/_\ABC ` with the vertices `A(alpha, 1,3),B(-2,beta, -5) and C(4,7,gamma)` find the value of `alpha, beta,gamma`

The origin is the centroid of /_\ABC with the vertices A(alpha, 1, 3),B(-2, beta, -5) and C(4,7,gamma) find the values of alpha, beta, gamma .

If the centroid of a triangle with vertices (alpha, 1, 3), (-2, beta, -5) and (4, 7, gamma) is the origin then alpha beta gamma is equal to …..........

If the centroid of triangles formed by the vertices (1, 2, 3), (2, 1, 0) and (3, 1, 4) is (alpha, beta, gamma) then the value of [alpha]+[beta]+[gamma], where [ ] represents the greatest integer function, is _______.

If origin is the orthocentre of the triangle with vertices A(cos alpha,sin alpha),B(cos beta,sin beta),C(cos gamma,sin gamma) then cos(2 alpha-beta-gamma)+cos(2 beta-gamma-alpha)+cos(2 gamma-alpha-beta)=

If the centroid of the tetrahedron O-ABC, where A-=(alpha,5,6), B-=(1,beta,4) and C-=(3,2,gamma) is G(1,-1,2) , then: alpha^(2) + beta^(2) + gamma^(2)=

If alpha,beta,gamma are the real roots of the equation x^(3)-3ax^(2)+3bx-1=0 then the centroid of the triangle with vertices (alpha,(1)/(alpha))(beta,(1)/(beta)) and (gamma,1/ gamma) is at the point

alpha , beta , gamma are the roots of the equation x^(3)-3x^(2)+6x+1=0 . Then the centroid of the triangle whose vertices are (alpha beta,1/(alpha beta)) , (beta gamma, 1/(beta gamma)) , (gamma alpha,1/(gamma alpha)) is

If the roots of 4-3x+5x^2+x^3=0 are alpha,beta,gamma then the value of 1/alpha+1/beta+1/gamma= ________ .

If alpha, beta gamma are the real roots of the equation x^(3)-3px^(2)+3qx-1=0 , then find the centroid of the triangle whose vertices are (alpha, (1)/(alpha)), (beta, (1)/(beta)) and (gamma, (1)/(gamma)) .

Let cos(alpha-beta) + cos(beta - gamma) + cos(gamma - alpha)= -3/2 , then the value of cos alpha + cos beta + cos gamma is